https://doi.org/10.1140/epjs/s11734-025-01581-4
Regular Article
Fractal dimension analysis for improved decision-making in non-stationary multi-arm bandit problems: a machine learning approach
1
Department of Computer Applications, School of Computer Science Engineering and Information Systems, Vellore Institute of Technology, 632014, Vellore, Tamil Nadu, India
2
School of Computer Science Engineering and Information Systems, Vellore Institute of Technology, 632014, Vellore, Tamil Nadu, India
a arunpandian.j@vit.ac.in, aparunpandian@gmail.com
Received:
14
October
2024
Accepted:
14
March
2025
Published online:
5
April
2025
In this research, we propose a novel approach to addressing the exploration–exploitation dilemma in multi-armed bandit (MAB) algorithms using fractal dimensions. The fractal dimension is used in the algorithms to represent the reward distributions of arms which represents the uncertainty of the arm in receiving the reward. The fractal dimension of the reward distribution is implemented in the most popular MAB optimization algorithms, such as Epsilon-Greedy, Upper Confidence Bound (UCB), Exponential-weight algorithm for Exploration and Exploitation (EXP3), and Thompson Sampling in this study. The algorithm prefers to choose arm with the least fractal dimension, as a lower fractal dimension represents less uncertainty of the arm. The performance of the fractal-enhanced MAB optimization algorithms is compared with traditional algorithms in non-stationary environments with various numbers of arms. The proposed approach provides a novel way to quantify and utilize the uncertainty of each arm in MAB problems.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
